Voltage reference circuits for providing constant voltage references or temperature dependent voltage references are well known in the art. Typically these circuits are provided as bandgap circuits which are designed to operably sum two voltages with opposite temperature slopes so as to provide the output reference voltage. One of the voltages is a Complementary-To-Absolute Temperature (CTAT) voltage typically provided by a base-emitter voltage of a forward biased bipolar transistor whose response is temperature dependent and reduces with increasing temperatures. The other is a Proportional-To-Absolute Temperature (PTAT) voltage which may be typically derived from the base-emitter voltage differences of two bipolar transistors operating at different collector current densities. As a PTAT voltage it will be understood that the output voltage will increase in relation to increasing temperatures. When the summed PTAT voltage and the CTAT voltage are balanced together the voltage is at a first order temperature insensitive. While being advantageous in providing reliable reference voltages and very common within the art, voltage reference circuits provided by traditional bandgap reference voltage circuits are sensitive to semiconductor process variations.
An example of a prior art bandgap reference voltage circuit 100 is illustrated in FIG. 1. This circuit is exemplary of the type of prior art circuitry which is sensitive to process variations. Disadvantages associated with such process variation sensitivities include the fact that the reference voltage generated may vary from process to process, lot to lot and even from die to die in the same wafer. This is obviously not a satisfactory arrangement.
The bandgap reference voltage circuit 100 of FIG. 1 includes a first PNP bipolar transistor Q1 operating at first collector current density and a second PNP bipolar transistor Q2 operating at a second collector current density which is less than that of the first collector current density. The emitter of the first bipolar transistor Q1 is coupled to the inverting input of an operational amplifier A and the emitter of the second bipolar transistor Q2 is coupled via a resistor r1 to the non-inverting input of the amplifier A. A third bipolar transistor Q3 is coupled to a reference voltage node ref via a second resistor r2. The collector current density difference between Q1 and Q2 may be established by having the emitter area of the second bipolar transistor Q2 larger than the emitter area of the first bipolar transistor Q1. Alternatively multiple transistors may be provided in each leg, with the sum of the collector currents of each of the transistors in a first leg being greater than that in a second leg. As a consequence of the differences in collector current densities between the bipolar transistors Q1 and Q2 a base-emitter voltage difference (ΔVbe) is developed across the resistor r1.
                              Δ          ⁢                                          ⁢                      V            be                          =                                            kT              q                        ⁢                          ln              ⁡                              (                n                )                                              =                      Δ            ⁢                                                  ⁢                                          V                be                            ⁡                              (                                  T                  0                                )                                      *                          T                              T                0                                                                        (        1        )            
Where:                k is the Boltzmann constant;        q is the charge on the electron,        T is operating temperature in Kelvin,        T0 is reference temperature, usually room temperature,        ΔVbe(T0) is base-emitter voltage difference at T0,        n is the collector current density ratio of Q1 and Q2.        
This voltage difference (ΔVbe) is of the form of a proportional to absolute temperature (PTAT) voltage. The voltage at the non-inverting input of the amplifier A is related to the base-emitter voltage difference (ΔVbe), and as a consequence the amplifier A forces the voltage at the inverting input to be equal to the voltage at the non-inverting input. The output of the amplifier A drives the gates of three PMOS transistors MP1, MP2, and MP3 which are arranged to mirror the PTAT current which flows through r1 such that the drain current of the three PMOS transistors are PTAT.
                              I          p                =                                            Δ              ⁢                                                          ⁢                              V                be                                                    r              1                                =                                                    Δ                ⁢                                                                  ⁢                                                      V                    be                                    ⁡                                      (                                          T                      0                                        )                                                                              r                1                                      *                          T                              T                0                                                                        (        2        )            
The drain current of MP3 flows through r2 resulting in a PTAT (ΔVbe) voltage across r2. The voltage at the reference voltage node ref is the summation of the base-emitter voltage (CTAT) of the bipolar transistor Q3 and the base emitter voltage difference ΔVbe voltage (PTAT) developed across r2 due to the PTAT current from MP3.
                              V          ref                =                                                            V                be                            ⁡                              (                                  Q                  ⁢                                                                          ⁢                  3                                )                                      +                                          I                PTAT                            *                              r                2                                              =                                                    V                be                            ⁡                              (                                  Q                  ⁢                                                                          ⁢                  3                                )                                      +                          Δ              ⁢                                                          ⁢                              V                                  be                  ⁢                                                                          ⁢                  0                                            *                              T                                  T                  0                                            *                                                r                  2                                                  r                  1                                                                                        (        3        )            
It is clear from equation 3 that the reference voltage at node ref has a base-emitter Vbe component and a base emitter voltage difference ΔVbe component. The Vbe component is inherently temperature dependent and is also subject to semiconductor process dependencies. Thus, the reference voltage may vary significantly from process to process, lot to lot and even from die to die in the same wafer.
The base-emitter voltage temperature dependence is given by equation 4:
                                          V            be                    ⁡                      (            T            )                          =                              V                          G              ⁢                                                          ⁢              0                                -                                    (                                                V                                      G                    ⁢                                                                                  ⁢                    0                                                  -                                                      V                                          be                      ⁢                                                                                                                            ⁡                                      (                                          T                      0                                        )                                                              )                        *                          T                              T                0                                              -                      m            *                          kT              q                        *                          ln              ⁡                              (                                  T                                      T                    0                                                  )                                              +                                    kT              q                        *                          ln              ⁡                              (                                                      j                    c                                                        j                                          c                      ⁢                                                                                          ⁢                      0                                                                      )                                                                        (        4        )            
Where:                VG0 is an extrapolated bandgap voltage from T0 to 0K,        Vbe(T0) is the base-emitter voltage at T0,        m is a temperature constant, typically denoted as XTI in computer simulation programs,        jc is collector current density at actual temperature, T, and        jc0 is collector current density at T0.        
The first two terms of equation 4 correspond to a linear variation against temperature and the last two terms correspond to a non-linear variation, usually denoted as curvature voltage Vcurv.
                              V          curv                =                                            -              m                        *                          kT              q                        *                          ln              ⁡                              (                                  T                                      T                    0                                                  )                                              +                                    kT              q                        *                          ln              ⁡                              (                                                      j                    c                                                        j                                          c                      ⁢                                                                                          ⁢                      0                                                                      )                                                                        (        5        )            
The reference voltage temperature dependence based on equations 3, 4 and 5 is given by equation 6:
                              V          ref                =                              V                          G              ⁢                                                          ⁢              0                                -                                    (                                                V                                      G                    ⁢                                                                                  ⁢                    0                                                  -                                                      V                                          be                      ⁢                                                                                                                            ⁡                                      (                                          T                      0                                        )                                                  -                                  Δ                  ⁢                                                                          ⁢                                      V                                          be                      ⁢                                                                                          ⁢                      0                                                        *                                                            r                      2                                                              r                      1                                                                                  )                        *                          T                              T                0                                              +                      V            curv                                              (        6        )            
To cancel the linear terms in equation 6 it is necessary to arrange that the following condition is met:
                              V                      G            ⁢                                                  ⁢            0                          =                                            V              be                        ⁡                          (                              T                0                            )                                +                      Δ            ⁢                                                  ⁢                          V                              be                ⁢                                                                  ⁢                0                                      *                                          r                2                                            r                1                                                                        (        7        )            
Then the reference voltage value corresponds to the extrapolated bandgap voltage, VG0 plus a small curvature term, Vcurv. One of the main disadvantages of this circuit design is that the reference voltage value corresponds to an unknown parameter, VG0, of about 1.1V to 1.22V, with large variation from process to process, lot to lot and even from die to die in the same wafer. This variation is translated into a large spread of the resultant reference voltage values and also of its Thermal Coefficient (TC). In order to compensate for this variation large trimming ranges are required to achieve both the desired absolute value output from the circuit and also and to maintain its TC within desired operating parameters.
There is therefore a need to provide a voltage reference circuit which provides a reference voltage which has less dependency on semiconductor process variations compared to traditional bandgap based reference voltage.